To do a brief asside. I've been playing a game called Final Fantasy Explorers recently, its a pretty fun game, its basically FFXIV/Monster hunter lite on the 3ds, where you team up and run dungeons with aoe telegraphs on enemy attacks and fight bosses with specific mechanics.
Blue Mage exists within this game, and it actually has less total spells than black mage, all of its spells can easily be learned by finding and fighting the monsters that use its skills, and these skills when put together for a cohesive kit of a support dps class. Is this Blue Mage "not a real blue mage" or only appealing to blue puristst? No. Its its own thing. Thats what really boils my piss about all of this, "can play something named BLU" arguments people make up. Blu is a class that conforms to the game environment its put in, and has wildly different usefulness and identity from game to game. This is why, in a game like ffxiv, I was looking forward to seeing what their interpretation would be, and they came out with limited blu, which is something that really does not appeal to me, but having an option to have both limited as side content and a balanced blu in the full game, does not take anything away from either, and neither is less or more a "real blue mage"